During hemodialysis, impurities and toxins are removed from the blood of a patient by drawing the blood out of the patient through a blood access site, typically via a catheter, and then passing the blood through an artificial kidney (often referred to as a “dialyzer”). The artificial kidney includes a semi-permeable membrane that separates a first conduit from a second conduit. Generally, a dialysis solution (often referred to as a “dialysate”) is flowed through the first conduit of the dialyzer while the patient's blood is flowed through the second conduit of the dialyzer, causing impurities and toxins to be transferred from the blood to the dialysate through the semi-permeable membrane. The impurities and toxins can, for example, be removed from the blood by a diffusion process. After passing through the dialyzer, the purified blood is then returned to the patient.